It would be the first summit in more than a decade between Korean leaders. Mr Moon said the Koreas should “make it happen” and encouraged the North to return to negotiations with the US.

But Pyongyang’s nuclear programme will hang over any attempts to bring the countries closer together.

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Media captionKim Yo-jong presented President Moon Jae-in with a folder holding a handwritten note from her brother, the leader of North Korea

The US administration has sought to maintain pressure on North Korea through sanctions and tough rhetoric from President Donald Trump.

Speaking to reporters during a flight on Saturday, Mr Pence said: “There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile programme.”